相关论文: Minimal pseudo-Anosov stretch factors on nonorient…

A foliation is R-covered if the leaf space in the universal cover is homeomorphic to the real numbers. We show that, up to topological conjugacy, there are at most two pseudo-Anosov flows transverse to such a foliation. If there are two,…

We study the minimal dilatation of pseudo-Anosov pure surface braids and provide upper and lower bounds as a function of genus and the number of punctures. For a fixed number of punctures, these bounds tend to infinity as the genus does. We…

We construct the first known examples of nontrivial, normal, all pseudo-Anosov subgroups of mapping class groups of surfaces. Specifically, we construct such subgroups for the closed genus two surface and for the sphere with five or more…

Let $F',F$ be any two closed orientable surfaces of genus $g'>g\ge 1$, and $f:F\to F$ be any pseudo-Anosov map. Then we can "extend" $f$ to be a pseudo-Anosov map $f':F'\to F'$ so that there is a fiber preserving degree one map $M(F',f')\to…

A classification of spanning surfaces for alternating links is provided up to genus, orientability, and a new invariant that we call aggregate slope. That is, given an alternating link, we determine all possible combinations of genus,…

We show that a pseudo-Anosov map on a boundary component of an irreducible 3-manifold has a power that partially extends to the interior if and only if its (un)stable lamination is a projective limit of meridians. The proof is through…

In this note, we use a result of Osserman and Schiffer \cite{OS} to give a variational characterization of the catenoid. Namely, we show that subsets of the catenoid minimize area within a geometrically natural class of minimal annuli. To…

We introduce a new technique, based on Gaussian maps, to study the possibility, for a given surface, to lie on a threefold as a very ample divisor with given normal bundle. We give several applications, among which one to surfaces of…

Using results relating taut foliations and pseudo-Anosov flows, we find cusped hyperbolic 3-manifolds which are not the non-singular part of a pseudo-Anosov flow. In particular, we find the first examples of cusped hyperbolic 3-manifolds…

Starting with a pseudo-Anosov flow $\varphi$ on a closed hyperbolic $3$-manifold $M$ and an embedded surface $S \subset M$ that is (almost) transverse to $\varphi$, we relate the hyperbolic geometry of $M$ (e.g. volume, circumference, short…

We give a new proof of a result by Fathi, which states that, to any homeomorphism of a closed surface which is isotopic to a pseudo-Anosov homeomorphism, we can associate a stable and an unstable invariant partition of the surface with…

We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays…

It has been known since 1981 that if one fixes an orientable surface $S$ of genus $g$, then there is a real number $\lambda_{min,g} > 1$ that is the dilatation of a pA diffeomorphism of $S$, and every other pA diffeomorphism of $S$ has…

We study the dynamics of measurable pseudo-Anosov homeomorphisms of surfaces, a generalization of Thurston's pseudo-Anosov homeomorphisms. A measurable pseudo-Anosov map has a transverse pair of full measure turbulations consisting of…

We study the dynamics of Topologically Anosov homeomorphisms of non compact surfaces. In the case of surfaces of genus zero and finite type, we classify them. We prove that if $f:S \to S$, is a Topologically Anosov homeomorphism where $S$…

A pseudo-Anosov mapping class acts on Teichm\"uller space $\mathcal{T}$ as well as on the curve graph $\mathcal{C}$ with so called north-south dynamics. We can measure a stable translation length $l_\mathcal{T}$ and $l_\mathcal{C}$ of the…

How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial closed curves, pants decompositions, and cut graphs with a given…

We first prove rigidity results for pseudo-Anosov flows in prototypes of toroidal 3-manifolds: we show that a pseudo-Anosov flow in a Seifert fibered manifold is up to finite covers topologically equivalent to a geodesic flow and we show…

We construct diffeomorphisms of ``pseudo-Anosov type'' on K3 surfaces M. In particular we obtain infinitely many examples of such diffeomorphisms that minimize entropy in their homotopy class, and for which neither the diffeomorphism nor…

In this article, we investigate short topological decompositions of non-orientable surfaces and provide algorithms to compute them. Our main result is a polynomial-time algorithm that for any graph embedded in a non-orientable surface…